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- Integrate by partial fractions
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Rewrite the fraction $\frac{1}{\left(x-1\right)^2\left(x+4\right)^2}$ in $4$ simpler fractions using partial fraction decomposition
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$\frac{1}{25\left(x-1\right)^2}+\frac{1}{25\left(x+4\right)^2}+\frac{-2}{125\left(x-1\right)}+\frac{2}{125\left(x+4\right)}$
Learn how to solve problems step by step online. Find the integral int(1/((x-1)^2(x+4)^2))dx. Rewrite the fraction \frac{1}{\left(x-1\right)^2\left(x+4\right)^2} in 4 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{1}{25\left(x-1\right)^2}+\frac{1}{25\left(x+4\right)^2}+\frac{-2}{125\left(x-1\right)}+\frac{2}{125\left(x+4\right)}\right)dx into 4 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{1}{25\left(x-1\right)^2}dx results in: \frac{-1}{25\left(x-1\right)}. The integral \int\frac{1}{25\left(x+4\right)^2}dx results in: \frac{-1}{25\left(x+4\right)}.
